Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Concept explainers

Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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Question

Use the approach in Gauss's Problem to find the following sums of arithmetic sequences. 

A. 1+2+3+4+...+1001

 

### Arithmetic Series Sums Using Gauss's Approach Gauss's approach to summing arithmetic series involves recognizing patterns in the sequences and applying a formula for efficiency. #### Problem 1.1.A-1 Use the approach in Gauss's **Problem** to find the following sums of arithmetic sequences: #### Questions: **a.** \(1 + 2 + 3 + 4 + \ldots + 1001\) **b.** \(1 + 3 + 5 + 7 + \ldots + 103\) **c.** \(8 + 17 + 26 + 35 + \ldots + 890\) **d.** \(293 + 290 + 287 + 284 + \ldots + 2\) #### Example Solution: **a. The sum of the sequence is** \[ \boxed{} \] ### Instructions: 1. Enter your answer in the answer box and then click **Check Answer**. ### Assessment: You have **3 parts** remaining to complete. Utilize the concepts of arithmetic sums, identify common differences, first and last terms of the sequences, and apply the formula for the sum of an arithmetic series: \[ S_n = \frac{n}{2} \times (a + l) \] where: - \( S_n \) is the sum of the arithmetic series, - \( n \) is the number of terms, - \( a \) is the first term, - \( l \) is the last term. You are encouraged to solve each part step-by-step and verify your results. Good luck!
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Transcribed Image Text:### Arithmetic Series Sums Using Gauss's Approach Gauss's approach to summing arithmetic series involves recognizing patterns in the sequences and applying a formula for efficiency. #### Problem 1.1.A-1 Use the approach in Gauss's **Problem** to find the following sums of arithmetic sequences: #### Questions: **a.** \(1 + 2 + 3 + 4 + \ldots + 1001\) **b.** \(1 + 3 + 5 + 7 + \ldots + 103\) **c.** \(8 + 17 + 26 + 35 + \ldots + 890\) **d.** \(293 + 290 + 287 + 284 + \ldots + 2\) #### Example Solution: **a. The sum of the sequence is** \[ \boxed{} \] ### Instructions: 1. Enter your answer in the answer box and then click **Check Answer**. ### Assessment: You have **3 parts** remaining to complete. Utilize the concepts of arithmetic sums, identify common differences, first and last terms of the sequences, and apply the formula for the sum of an arithmetic series: \[ S_n = \frac{n}{2} \times (a + l) \] where: - \( S_n \) is the sum of the arithmetic series, - \( n \) is the number of terms, - \( a \) is the first term, - \( l \) is the last term. You are encouraged to solve each part step-by-step and verify your results. Good luck!
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